Finite Group Databasebeta

← #11872794

Subgroups — #11872794

Order 1152.

1182 conjugacy classes of subgroups.

The subgroup lattice has 528 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596202C211yesmaximal, characteristic, complemented
2#10596016C211yesmaximal, characteristic
3C32×#461C211yesmaximal, characteristic, complemented
4#10592868C211yesmaximal, characteristic
5#10592868C211yesmaximal, characteristic
6#10592863C211yesmaximal, characteristic, complemented
7SD16×C3⋊Dic3C211yesmaximal, characteristic, complemented
8#10592782C211yesmaximal, characteristic, complemented
9#10592708C211yesmaximal, characteristic, complemented
10#10592546C211yesmaximal, characteristic, complemented
11#10592539C211yesmaximal, characteristic, complemented
12#10592516C211yesmaximal, characteristic, complemented
13#10592514C211yesmaximal, characteristic, complemented
14#10592513C211yesmaximal, characteristic, complemented
15#10592487C211yesmaximal, characteristic, complemented
16#80413—34nomaximal
17C2×D4×C3⋊D3C2211yescharacteristic
18C2×C32×SD16C2211yescharacteristic
19C2×C32×SD16C2211yescharacteristic
20C32×C4⋊Q8C2211yescharacteristic, complemented
21C32×C4×D4C2211yescharacteristic
22#64155C2211yescharacteristic
23#64155C2211yescharacteristic
24Q8×C3⋊Dic3C2211yescharacteristic, complemented
25Q8×C3⋊Dic3C2211yescharacteristic, complemented
26C2×#3755C2211yescharacteristic
27C2×#3755C2211yescharacteristic
28D4×C3⋊Dic3C2211yescharacteristic
29C4×#638—21no—
30C2×#3752—21no—
31#64107—21no—
32#64107—21no—
33#64102C2211yescharacteristic
34#64101C2211yescharacteristic
35#64098—21no—
36#64098—21no—
37#64090—21no—
38C22⋊C4×C3⋊D3—21no—
39C4×C4⋊(C3⋊D3)C2211yescharacteristic
40#64081C2211yescharacteristic
41#64079C2211yescharacteristic, complemented
42C32×C4⋊C8C2211yescharacteristic, complemented
43C32×#103C2211yescharacteristic, complemented
44C32×#103C2211yescharacteristic, complemented
45#63662C2211yescharacteristic, complemented
46#63662C2211yescharacteristic, complemented
47#63659C2211yescharacteristic
48#63659C2211yescharacteristic
49#63648C2211yescharacteristic
50#63648C2211yescharacteristic
51#63647C2211yescharacteristic
52#63647C2211yescharacteristic
53#63645C2211yescharacteristic, complemented
54#63644C2211yescharacteristic, complemented
55#63642C2211yescharacteristic, complemented
56C8×C3⋊Dic3C2211yescharacteristic, complemented
57#63635C2211yescharacteristic, complemented
58#63634C2211yescharacteristic, complemented
59C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic, complemented
60#5731—34no—
61#5545—34no—
62C3×#461D314yescomplemented
63#5169—34no—
64#5169—34no—
65#5164—34no—
66Dic3×SD16—34no—
67#5083—34no—
68#5009—34no—
69#4847—34no—
70#4840—34no—
71#4817—34no—
72#4815—34no—
73#4814—34no—
74#4788—34no—
75C23×C3⋊D3—21no—
76C2×C32×Q8C2311yescharacteristic
77C2×C32×Q8C2311yescharacteristic
78C2×C32×D4C2311yescharacteristic
79C22×C32×C4—21no—
80C2×#638—21no—
81C22×C3⋊Dic3—21no—
82D4×C3⋊D3—22no—
83D4×C3⋊D3—22no—
84C2×C4⋊(C3⋊D3)C2311yescharacteristic
85C2×C4×C3⋊D3—21no—
86C2×C4×C3⋊D3—21no—
87C2×C4×C3⋊D3C2311yescharacteristic
88C32×SD16—22no—
89C32×SD16—22no—
90C2×C32×C8C2311yescharacteristic
91C2×C32×C8C2311yescharacteristic
92C32×C4⋊C4—21no—
93C32×C4⋊C4—21no—
94C32×C4⋊C4C2311yescharacteristic
95C32×C22⋊C4—21no—
96C32×C42C2311yescharacteristic
97#3757—21no—
98#3755—22no—
99#3755—22no—
100#3752—21no—
101#3752—21no—
102#3752—21no—
103#3752—21no—
104#3752—21no—
105#3752D411yescharacteristic
106#3752D411yescharacteristic
107C4⋊(C3⋊Dic3)—21no—
108C4⋊(C3⋊Dic3)—21no—
109C4⋊(C3⋊Dic3)C2311yescharacteristic
110C4⋊(C3⋊Dic3)C2311yescharacteristic
111C4⋊(C3⋊Dic3)C2311yescharacteristic
112#3750—21no—
113#3750—21no—
114#3750—21no—
115#3750—21no—
116#3750D411yescharacteristic
117#3750D411yescharacteristic
118C4×C3⋊Dic3—21no—
119C4×C3⋊Dic3—21no—
120C4×C3⋊Dic3—21no—
121C4×C3⋊Dic3C2311yescharacteristic
122C2×C3⋊(C3⋊C8)C2311yescharacteristic
123C2×C3⋊(C3⋊C8)C2311yescharacteristic
124#3123—91noSylow
125C2×D3×D4—34no—
126C2×C3×SD16C2×D314yes—
127C2×C3×SD16C2×D314yes—
128C3×C4⋊Q8C2×D314yescomplemented
129C3×C4×D4C2×D314yes—
130#946—34no—
131#946—34no—
132Q8×Dic3—34no—
133Q8×Dic3—34no—
134C2×#215—34no—
135C2×#215—34no—
136D4×Dic3—34no—
137C4×#67—64no—
138C2×(C2×D3)⋊C4—64no—
139#898—64no—
140#898—64no—
141#893—34no—
142#892—34no—
143#889—64no—
144#889—64no—
145#67⋊C4—64no—
146D3×C22⋊C4—64no—
147C4×D12—34no—
148#872—34no—
149#870—34no—
150C3×C4⋊C8C2×D314yescomplemented
151C3×#103C2×D314yescomplemented
152C3×#103C2×D314yescomplemented
153#835—34no—
154#835—34no—
155#832—34no—
156#832—34no—
157#821—34no—
158#821—34no—
159(C2×D3)⋊C8—34no—
160(C2×D3)⋊C8—34no—
161#818—34no—
162#817—34no—
163#815—34no—
164C8×Dic3—34no—
165#808—34no—
166#807—34no—
167C4⋊(C3⋊C8)—34no—
168C23×C32—21no—
169C22×C3⋊D3—21no—
170C22×C3⋊D3—24no—
171C22×C3⋊D3—81no—
172C22×C3⋊D3—81no—
173C22×C3⋊D3C2×D411yescharacteristic
174C32×Q8—21no—
175C32×Q8—21no—
176C32×Q8—21no—
177C32×Q8—21no—
178C32×D4—21no—
179C32×D4#4112yes—
180C2×C32×C4—21no—
181C2×C32×C4—21no—
182C2×C32×C4—21no—
183C2×C32×C4—81no—
184C2×C32×C4C2×D411yescharacteristic
185C2×C32×C4C2×D411yescharacteristic
186C2×C32×C4C2411yescharacteristic
187#638—24no—
188C2×C3⋊Dic3—21no—
189C2×C3⋊Dic3—21no—
190C2×C3⋊Dic3—21no—
191C2×C3⋊Dic3—81no—
192C2×C3⋊Dic3C2×D411yescharacteristic
193C2×C3⋊Dic3C2×D411yescharacteristic
194C2×C3⋊Dic3C2×D411yescharacteristic
195C4⋊(C3⋊D3)—21no—
196C4⋊(C3⋊D3)#4112yes—
197C4×C3⋊D3—21no—
198C4×C3⋊D3—21no—
199C4×C3⋊D3—81no—
200C4×C3⋊D3—81no—
201C32×C8—21no—
202C32×C8—21no—
203C3⋊(C3⋊C8)—21no—
204C3⋊(C3⋊C8)—21no—
205#541—91no—
206#518—91no—
207#485—91no—
208#485—91no—
209#478—91no—
210#478—91no—
211#461—91no—
212#461C3⋊D311yescharacteristic, complemented
213#450—91no—
214#450—91no—
215#440—91no—
216#440—91no—
217C4×SD16—91no—
218C4×SD16—91no—
219#433—91no—
220C23×D3—64no—
221C2×C3×Q8C22×D314yes—
222C2×C3×Q8C22×D314yes—
223C2×C3×D4C22×D314yes—
224C22×C3×C4—24no—
225C2×#67—64no—
226C22×Dic3—64no—
227D3×D4—68no—
228D3×D4—68no—
229C2×D12—34no—
230C2×C4×D3—34no—
231C2×C4×D3—64no—
232C2×C4×D3—64no—
233C3×SD16—28no—
234C3×SD16—28no—
235C2×C3×C8C22×D314yes—
236C2×C3×C8C22×D314yes—
237C3×C4⋊C4—24no—
238C3×C4⋊C4—24no—
239C3×C4⋊C4C22×D314yes—
240C3×C22⋊C4—24no—
241C3×C42C22×D314yes—
242#217—64no—
243#215—68no—
244#215—68no—
245(C2×D3)⋊C4—34no—
246(C2×D3)⋊C4—34no—
247(C2×D3)⋊C4—64no—
248(C2×D3)⋊C4—64no—
249(C2×D3)⋊C4—64no—
250(C2×D3)⋊C4—64no—
251(C2×D3)⋊C4—64no—
252C4⋊Dic3—34no—
253C4⋊Dic3—34no—
254C4⋊Dic3—34no—
255C4⋊Dic3—64no—
256C4⋊Dic3—64no—
257Dic3⋊C4—34no—
258Dic3⋊C4—34no—
259Dic3⋊C4—64no—
260Dic3⋊C4—64no—
261Dic3⋊C4—64no—
262Dic3⋊C4—64no—
263C4×Dic3—34no—
264C4×Dic3—64no—
265C4×Dic3—64no—
266C4×Dic3—64no—
267C2×C3⋊C8—34no—
268C2×C3⋊C8—34no—
269C22×C32—22no—
270C22×C32—41no—
271C22×C32—41no—
272C22×C32C22×D411yescharacteristic
273C2×C3⋊D3—21no—
274C2×C3⋊D3—22no—
275C2×C3⋊D3—21no—
276C2×C3⋊D3—21no—
277C2×C3⋊D3—41no—
278C2×C3⋊D3—41no—
279C2×C3⋊D3—84no—
280C32×C4—21no—
281C32×C4—21no—
282C32×C4—41no—
283C32×C4—41no—
284C32×C4—41no—
285C32×C4C2×#4111yescharacteristic
286C32×C4C2×#4111yescharacteristic
287C3⋊Dic3—21no—
288C3⋊Dic3—21no—
289C3⋊Dic3—21no—
290C3⋊Dic3—41no—
291C3⋊Dic3—41no—
292C3⋊Dic3—41no—
293C22×D4—91no—
294C2×SD16—91no—
295C2×SD16—91no—
296C2×SD16C2×C3⋊D311yescharacteristic
297C2×SD16C2×C3⋊D311yescharacteristic
298C4⋊Q8C2×C3⋊D311yescharacteristic, complemented
299#126—181no—
300#126—181no—
301#125—91no—
302#125—181no—
303#125—181no—
304C22⋊Q8—91no—
305C22⋊Q8—91no—
306C4×Q8—91no—
307C4×Q8—91no—
308C4×D4—91no—
309C4×D4—91no—
310C4×D4—91no—
311C4×D4—181no—
312C4×D4—181no—
313C4×D4C2×C3⋊D311yescharacteristic
314#117—91no—
315#117—91no—
316C2×C22⋊C4—181no—
317C2×C22⋊C4—181no—
318#107—91no—
319#107—91no—
320#106—91no—
321#106—91no—
322C4⋊C8—91no—
323C4⋊C8C2×C3⋊D311yescharacteristic, complemented
324#103—91no—
325#103—91no—
326#103C2×C3⋊D311yescharacteristic, complemented
327#103C2×C3⋊D311yescharacteristic, complemented
328#102—91no—
329#102—91no—
330#102—91no—
331#102—91no—
332C22⋊C8—91no—
333C22⋊C8—91no—
334#97—91no—
335C4×C8—91no—
336C23×C3—24no—
337C22×D3—34no—
338C22×D3—64no—
339C22×D3—616no—
340C22×D3—244no—
341C22×D3—244no—
342C3×Q8—24no—
343C3×Q8—24no—
344C3×Q8—24no—
345C3×Q8—24no—
346C3×D4—24no—
347C3×D4#23718yes—
348C2×C3×C4—24no—
349C2×C3×C4—24no—
350C2×C3×C4—24no—
351C2×C3×C4—84no—
352C2×C3×C4D3×D414yes—
353C2×C3×C4D3×D414yes—
354C2×C3×C4C23×D314yes—
355#67—616no—
356C2×Dic3—34no—
357C2×Dic3—34no—
358C2×Dic3—34no—
359C2×Dic3—64no—
360C2×Dic3—64no—
361C2×Dic3—64no—
362C2×Dic3—244no—
363D12—38no—
364D12—64no—
365C4×D3—64no—
366C4×D3—64no—
367C4×D3—244no—
368C4×D3—244no—
369C3×C8—24no—
370C3×C8—24no—
371C3⋊C8—64no—
372C3⋊C8—64no—
373C2×C32—42no—
374C2×C32#52511yescharacteristic
375C2×C32#57711yescharacteristic
376C2×C32#57711yescharacteristic
377C3⋊D3—41no—
378C3⋊D3—42no—
379C24—181no—
380C2×Q8C22×C3⋊D311yescharacteristic
381C2×Q8C22×C3⋊D311yescharacteristic
382C2×D4—91no—
383C2×D4—181no—
384C2×D4—182no—
385C2×D4—182no—
386C2×D4C22×C3⋊D311yescharacteristic
387C22×C4—21no—
388C22×C4—91no—
389C22×C4—181no—
390C22×C4—181no—
391C22×C4—181no—
392SD16—22no—
393SD16—22no—
394SD16—182no—
395SD16—182no—
396C2×C8—91no—
397C2×C8—91no—
398C2×C8C22×C3⋊D311yescharacteristic
399C2×C8C22×C3⋊D311yescharacteristic
400C4⋊C4—21no—
401C4⋊C4—21no—
402C4⋊C4—91no—
403C4⋊C4—91no—
404C4⋊C4—91no—
405C4⋊C4—91no—
406C4⋊C4—91no—
407C4⋊C4—181no—
408C4⋊C4—181no—
409C4⋊C4—181no—
410C4⋊C4—181no—
411C4⋊C4—181no—
412C4⋊C4—181no—
413C4⋊C4C22×C3⋊D311yescharacteristic
414C22⋊C4—21no—
415C22⋊C4—91no—
416C22⋊C4—91no—
417C22⋊C4—181no—
418C22⋊C4—181no—
419C22⋊C4—181no—
420C22⋊C4—181no—
421C22⋊C4—181no—
422C22⋊C4—181no—
423C42—91no—
424C42—181no—
425C42—181no—
426C42—181no—
427C42C22×C3⋊D311yescharacteristic
428C22×C3—28no—
429C22×C3—44no—
430C22×C3—44no—
431C22×C3C2×D3×D414yes—
432C2×D3—64no—
433C2×D3—64no—
434C2×D3—64no—
435C2×D3—68no—
436C2×D3—124no—
437C2×D3—124no—
438C2×D3—2416no—
439C3×C4—24no—
440C3×C4—24no—
441C3×C4—44no—
442C3×C4—44no—
443C3×C4—44no—
444C3×C4C2×#23714yes—
445C3×C4D3×#4114yes—
446Dic3—64no—
447Dic3—64no—
448Dic3—64no—
449Dic3—124no—
450Dic3—124no—
451Dic3—124no—
452C32#312311yescharacteristic, complemented, Sylow
453C23—21no—
454C23—91no—
455C23—184no—
456C23—181no—
457C23—721no—
458C23—721no—
459Q8—21no—
460Q8—21no—
461Q8—21no—
462Q8—21no—
463D4—21no—
464D4—92no—
465D4—184no—
466D4—181no—
467D4#383012yes—
468C2×C4—21no—
469C2×C4—21no—
470C2×C4—21no—
471C2×C4—81no—
472C2×C4—91no—
473C2×C4—91no—
474C2×C4—91no—
475C2×C4—181no—
476C2×C4—181no—
477C2×C4—181no—
478C2×C4—181no—
479C2×C4—181no—
480C2×C4—721no—
481C2×C4—721no—
482C2×C4—721no—
483C2×C4D4×C3⋊D311yescharacteristic
484C2×C4D4×C3⋊D311yescharacteristic
485C2×C4C23×C3⋊D311yescharacteristic
486C8—21no—
487C8—21no—
488C8—181no—
489C8—181no—
490C2×C3—48no—
491C2×C3#560614yes—
492C2×C3#576214yes—
493C2×C3#577814yes—
494D3—124no—
495D3—128no—
496C22—22no—
497C22—41no—
498C22—41no—
499C22—181no—
500C22—181no—
501C22—181no—
502C22—182no—
503C22—361no—
504C22—361no—
505C22—724no—
506C22C2×D4×C3⋊D311yescharacteristic
507C4—21no—
508C4—21no—
509C4—41no—
510C4—41no—
511C4—41no—
512C4—181no—
513C4—181no—
514C4—181no—
515C4—361no—
516C4—361no—
517C4—361no—
518C4C2×#383011yescharacteristic
519C4#41×C3⋊D311yescharacteristic
520C3#8041314yescomplemented
521C2—42no—
522C2—361no—
523C2—362no—
524C2#1059607711yescharacteristic
525C2#1059623311yescharacteristic
526C2#1059624911yescharacteristic
subgroupG/H
centerC22C2×D4×C3⋊D3
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C23×C3⋊D3
FittingC32×#461C2
socleC22×C32C22×D4
prime radicalC2×D4×C3⋊D3C22
hypercenter#461C3⋊D3
hypocenterC32#3123
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ #461

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #10596202C2semidirect
3. C32×#461C2semidirect
6. #10592863C2semidirect
7. SD16×C3⋊Dic3C2semidirect
8. #10592782C2semidirect
9. #10592708C2semidirect
10. #10592546C2semidirect
11. #10592539C2semidirect
12. #10592516C2semidirect
13. #10592514C2semidirect
14. #10592513C2semidirect
15. #10592487C2semidirect
20. C32×C4⋊Q8C22semidirect
24. Q8×C3⋊Dic3C22semidirect
25. Q8×C3⋊Dic3C22semidirect
41. #64079C22semidirect
42. C32×C4⋊C8C22semidirect
43. C32×#103C22semidirect
44. C32×#103C22semidirect
45. #63662C22semidirect
46. #63662C22semidirect
53. #63645C22semidirect
54. #63644C22semidirect
55. #63642C22semidirect
56. C8×C3⋊Dic3C22semidirect
57. #63635C22semidirect
58. #63634C22semidirect
59. C4⋊(C3⋊(C3⋊C8))C22semidirect
62. C3×#461D3semidirect
128. C3×C4⋊Q8C2×D3semidirect
150. C3×C4⋊C8C2×D3semidirect
151. C3×#103C2×D3semidirect
152. C3×#103C2×D3semidirect
212. #461C3⋊D3semidirect
298. C4⋊Q8C2×C3⋊D3semidirect
323. C4⋊C8C2×C3⋊D3semidirect
326. #103C2×C3⋊D3semidirect
327. #103C2×C3⋊D3semidirect
452. C32#3123semidirect
520. C3#80413semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#105962022
#105960162
C32×#4612
#105928682
#105928632
SD16×C3⋊Dic32
#105927822
#105927082
#105925462
#105925392
#105925162
#105925142
#105925132
#105924872
#804133